Bound doctor diagnostics within client timeout

[brynary]

Summary

• cap each external doctor probe at 15 seconds and keep Docker at 5 seconds
• return provider-specific LLM timeout results while other provider checks complete
• cap the server diagnostics operation at 25 seconds so the existing 30-second client deadline receives a structured 504 response
• document the diagnostics 504 response in OpenAPI

Test plan

• cargo nextest run --workspace
• cargo nextest run -p fabro-server
• cargo nextest run -p fabro-cli doctor
• cargo +nightly-2026-04-14 clippy --workspace --all-targets -- -D warnings
• cargo +nightly-2026-04-14 fmt --check --all
• cargo build -p fabro-api
• bun run generate in lib/packages/fabro-api-client

Security

• the diagnostics route still requires RequiredUser
• the timeout response uses fixed text and does not expose upstream errors or credentials
• no new retries or outbound targets are added

[Copilot]

Pull request overview

This PR bounds the server “doctor/diagnostics” work so it reliably completes within the existing client deadline, returning a structured 504 when diagnostics exceed a capped duration, while still providing per-provider timeout results for external probes.

Changes:

• Added a server-side timeout wrapper for the diagnostics handler to return a structured 504 Gateway Timeout response.
• Capped external diagnostic probes (e.g., LLM providers, GitHub, Brave, Daytona) to 15s and Docker to 5s, with provider-specific timeout outcomes.
• Documented the new 504 response for diagnostics in the OpenAPI spec and added unit tests covering timeout behavior.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

File	Description
lib/apps/fabro-server/src/server/handler/system.rs	Wraps the diagnostics handler with a 25s timeout and returns a structured 504 on timeout; adds a test for the timeout response shape.
lib/apps/fabro-server/src/diagnostics.rs	Introduces shared timeout constants and applies them across external probes; adds helper(s) + tests for timeout reporting.
docs/public/api-reference/fabro-api.yaml	Documents the diagnostics 504 timeout response in OpenAPI.

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